Vuto: Gudumu la Tsiku Lobadwa
Kodi ndi kuzungulira kangati nambala ina isanabwerezedwe? Kochepa kwambiri kuposa mmene anthu ambiri amaganizira.
Vuto la tsiku lobadwa pa gudumu la tibowozipangizoKabowoChimodzi mwa tibowo 37 tokhala ndi manambala pa rotor. Kamatchedwanso: slot, cup.Werengani yonse → 37: pambuyo pa kuzungulira 8 kokha pali mwayi woposa theka woti nambala ina yatuluka kale kawiri. Osewera amaona kubwerezedwa ngati kalembedwe; ndi khalidwe loyembekezeka la gudumu lachilungamo.
Vuto
Zunguzani gudumu lachilungamo la ku Ulaya. Kodi ndi kuzungulira kangati mpaka kuthekeramasamuKuthekeraMwayi wa zotsatira, kuchokera 0 mpaka 1 kapena 0% mpaka 100%. Nambala imodzi: 1/37 = 2.70%.Werengani yonse → koti kuzungulira kawiri pang’ono kwaonetsa nambala yofanana kupitirire theka? Osewera ambiri amalingalira kwinakwake pafupi ndi 18 kapena 19, theka la 37. Yankho ndi 8.
Yankho
Werengerani kuthekera kwa kusabwerezedwa ndipo chotsani ku chimodzi. Pambuyo pa kuzungulira k, p(zonse zosiyana) = (37/37)(36/37)(35/37)…((38 − k)/37). Pa k = 8: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44, choncho p(kubwerezedwa kwina) ≈ 0.56. Pa k = 14 ndi 0.93; pa k = 20 ndi 0.996. Maganizo amalakwa chifukwa chiwerengero cha awiriawiri a kuzungulira chimakula ngati k², ndipo awiriawiri aliwonse angathe kufanana.
N’chifukwa chiyani zili zofunika pa tebulo
Bolodi la zotsatira la manambala 20 omaliza pafupifupi nthawi zonse lidzaonetsa kubwerezedwa kamodzi pang’ono, kawirikawiri kawiri kapena katatu. Osewera amaona “17 inatuluka kawiri pa kuzungulira khumi” ndipo amamaliza kuti 17 ikutentha; masamu a tsiku lobadwa amati kubwerezedwa mkati mwa kuzungulira khumi kumachitika 74% ya nthawi ndipo nambala yobwerezedwa ndi yachisawawa. Kalembedwe ndi kenikeni; tanthauzo si lenileni.
Vuto lotsatira
Kodi ndi kuzungulira kangati mpaka nambala inayake, tinene 17, itatuluka kawiri? Limenelo ndi funso losiyana lokhala ndi yankho lalikulu kwambiri: kudikira koyembekezeka ndi kuzungulira 74, ndipo kuthekera kwa 17 ziwiri mkati mwa kuzungulira 20 ndi pafupifupi 10%. Kusiyana pakati pa “nambala ina imabwerezedwa” (kuzungulira 8) ndi “nambala iyi imabwerezedwa” (kuzungulira 74) ndiko kusiyana konse pakati pa kalembedwe kamene mumazindikira pambuyo pake ndi kulosera kumene mumapanga pasadakhale.
Yesani
Yendetsani Masewera Oyesera pa kuzungulira khumi ndipo yang’anani mbiri. Kawirikawiri padzakhala kubwerezedwa. Yendetsaninso. Nambala yobwerezedwa idzakhala yosiyana. Chitani zimenezi ka khumi ndipo mwaona vuto la tsiku lobadwamasamuVuto la tsiku lobadwaKuchuluka kwa anthu kofunikira kuti awiri mwina agawane tsiku lobadwa, kapena kuchuluka kwa kuzungulira kuti nambala mwina ibwerezedwe. Pa gudumu la tibowo 37, kuzungulira 8 nkokwanira kuti mwayi upitirire theka.Werengani yonse →; chitani ka chikwi (zoyerekezera zingathe) ndipo mwaliyeza.
Fomula
Mafunso
Ndendende, ndi tibowo 37 m’malo mwa masiku 365. Anthu 23 amapereka 50% pa masiku obadwa; kuzungulira 8 kumapereka 56% pa gudumu.
50% pambuyo pa kuzungulira pafupifupi 19. Zidakali zachizolowezi.
Ayi. Kuzungulira masauzande kuchokera pa gudumu limodzi kukanatero; kubwerezedwa sikutero konse.
Masamu Osangalatsa
Yesani nokha choyamba. Yankho lililonse labisika; litsegulireni mukakonzeka.
Bolodi la zotsatira pafupi ndi gudumu la ku America likusonyeza kuzungulira 16 komaliza. Kodi n’kotheka bwanji kuti palibe nambala imene ikupezeka kawiri pa ilo?
Onetsani yankho
Yankho Pafupifupi 2.5%: pafupifupi mabolodi 39 pa 40 amasonyeza chobwerezedwa chimodzi kapena kuposerapo.
Pitani kuzungulira ndi kuzungulira. Kuzungulira koyamba kungakhale chilichonse. Kwachiwiri kuyenera kuiphonya: mwayi 37 pa 38. Kwachitatu kuyenera kuphonya zonse ziwiri: 36 pa 38. Kwakhumi ndi chisanu ndi chimodzi kuyenera kuphonya manambala khumi ndi asanu: 23 pa 38.
Chulukitsani: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246.
Bolodi lopanda chobwerezedwa ndilo losowa. Bolodi lokhala ndi chobwerezedwa silinena kanthu za gudumu.
Pa kuzungulira khumi kwa gudumu la ku Ulaya, kodi kuthekera kwakuti 17 ituluke kasanu ndendende ndi kotani? Kuti nambala inayake, nambala iliyonse, ituluke kasanu kapena kuposerapo? Ndipo kuti nambala inayake ituluke katatu kapena kuposerapo pa kuzungulira kanayi?
Onetsani yankho
Yankho 17 kasanu ndendende: 1 pa 315,576. Nambala inayake kasanu kapena kuposerapo: pafupifupi 1 pa 8,333. Nambala inayake katatu kapena kuposerapo pa kuzungulira kanayi: 1 pa 349.
17 kasanu: sankhani kuti ndi kuzungulira kuti kasanu mwa khumi, njira 252, iliyonse ndi kuthekera kwa (1/37)⁵ × (36/37)⁵. Pamodzi, 1 pa 315,576.
Nambala inayake: nambala iliyonse mwa 37 ili ndi kuthekera kwa 1 pa 308,325 kogunda kasanu kapena kuposerapo, zimene zimapereka 37 pa 308,325, kapena 1 pa 8,333. Nkhani yosowa ya manambala awiri iliyonse ikugunda kasanu imawerengedwa kawiri, koma kuichotsa sikusintha kanthu pa kulondola uku.
Katatu pa kuzungulira kanayi: pa nambala imodzi, 4 × 36 + 1 = 145 mwa zotsatira 37⁴ zotheka; pa nambala iliyonse mwa 37, 145/37³ = 1 pa 349.
Pa gudumu la zirogudumuZiroKabowo kamodzi kobiriwira kamene betcha la even-money, dazeni kapena mzati siliphimba; gwero la phindu la kasino. Imatchedwanso: ziro imodzi, 0.Werengani yonse → ziwiri, manambala ofananira ndi 1 pa 359,275, 1 pa 9,243 ndi 1 pa 368. Kusiyana pakati pa “17” ndi “nambala inayake” ndi vuto la tsiku lobadwamasamuVuto la tsiku lobadwaKuchuluka kwa anthu kofunikira kuti awiri mwina agawane tsiku lobadwa, kapena kuchuluka kwa kuzungulira kuti nambala mwina ibwerezedwe. Pa gudumu la tibowo 37, kuzungulira 8 nkokwanira kuti mwayi upitirire theka.Werengani yonse → kachiwiri: pali njira 37 zodabwitsidwira.
Nthabwala yopumitsa
China chake chimabwerezedwa msanga. China chakecho n’chachisawawa.
Magwero
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, mafunso a roulette.